Theory of Magnetic Disturbance by .Earth- Currents. 435 

 For we have clearly 







F„ 



F 





Also, since 



the 



number of cars per mile is constant, 









i_i' 









y y 



Moreover, 









ence 













F 



K _ ,!/ 2 _ 1 



Various interesting results may be obtained from the 

 simple formula (II.), which we may write 



F = x u 2 .7 g r ^ a 



^ V(4?/ 2 H-cr) 



Now if the number of cars per mile be constant the current 

 varies as the length of the line. Hence 



I = \a ; 



and 



y \/4:?f + a 2 



In this expression the distance y must be measured in 

 centimetres in order to give F w in absolute units. Hence we 

 must introduce in the denominator a factor 1*6 X 10°, or in the 

 numerator '62 X 10 -5 . Thus 



F p =' 62 iQ-5 ^ V C L_ 



4 y N /(4/ + a 2 ) / 



where the lengths are now all in miles. 10 -5 is an ordinary 

 unit in terrestrial magnetic work denoted by <y. 



With regard to the dimensions of this expression it must 

 be remembered that y^o? is a number and \a an electric 

 current. Thus /u, 2 and X both have dimensions in space, and 

 in the values given for the two quantities it is assumed that 

 each is referred to a mile run of line. 



Now according to Professor Riicker's Stockton experiments 

 the approximate value of /xa/2 is *64, where a = 2 miles. 



Hence 



^ = •64, ^ = -41. 



